相关论文: On a linear Gromov-Wasserstein distance

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

Pairwise comparison of graphs is key to many applications in Machine learning ranging from clustering, kernel-based classification/regression and more recently supervised graph prediction. Distances between graphs usually rely on…

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…

Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…

The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal…

The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW…

In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…

The Gromov-Wasserstein (GW) distance is an extension of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is specified as the solution of a non-convex quadratic program…

The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both distances are based on non-convex, quadratic optimal transport…

In the context of optimal transport methods, the subspace detour approach was recently presented by Muzellec and Cuturi (2019). It consists in building a nearly optimal transport plan in the measures space from an optimal transport plan in…

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…

This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex…

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…

The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…

We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which…

Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide…

Comparing graphs by means of optimal transport has recently gained significant attention, as the distances induced by optimal transport provide both a principled metric between graphs as well as an interpretable description of the…